(1) Field of the Invention
The present invention relates generally to the field of sonar signal processing and, more particularly, preferably comprises a multistage and automated method to measure the spatial arrangement among a very small number of measurements whereby an ascertainment of the mathematical property of randomness (or noise-degree) may be made.
(2) Description of the Prior Art
Naval sonar systems require that signals be classified according to structure; i.e., periodic, transient, random or chaotic. In many cases it may be highly desirable and/or critical to know whether data received by a sonar system is simply random noise, which may be a false alarm, or is more likely due to detection of a submarine or other vessel of interest.
Recent research has revealed a critical need for highly sparse-data-set statistical methods separate and apart from those treating large samples. It is well known that large sample methods often fail when applied to small sample distributions. In some cases, prior art statistical methods may label an obviously nonrandom distributions (e.g., see FIG. 2) as random. It is apparently not well known or appreciated that a single measurement system designed to detect stochastic randomness occasionally fails for certain distributions. For example, the method of U.S. patent application Ser. No. 09/934,343, now U.S. Pat. No. 6,597,634, which is incorporated herein by reference, fails to detect non-randomness in data such as displayed in FIG. 2. Most randomness assessment methods are applicable for truly random distributions, and sometimes fail to label correctly truly nonrandom distributions as pointed out by Dr. Rushkin (A. L. Rushkin, Testing Randomness: A Suite of Statistical Procedures, Theory of Probability and its Applications, 2000, vol. 45, no. 1, pp. 111-132). As an example, it is quite possible for the Runs Test (described below) to label an error-free constant two-dimensional function, such as f(x)=x, “nonrandom,” while an error-free linear function, such as f(x)=a+bx, is deemed “random.”
Very small data distributions may comprise data sets with approximately less than ten to fifteen data measurements. Such data sets can be analyzed mathematically with certain nonparametric discrete probability distributions as opposed to large-sample methods, which employ continuous probability distributions (such as the Gaussian).
Nonparametric statistics is a field that treats discrete variables or a quantitative variable whose set of possible values is countable. Typical examples of discrete variables are variables whose possible values are a subset of the integers, such as the number of bacteria in a microphotograph, discrete time increments [t0=0, t1=1, t2=2, . . . ], number of “heads” in 10 coin-flips, the USA population, ages rounded to the nearest year, or the number of pages in a DoD Technical Manual. Moreover, a random variable is discrete if and only if its cumulative probability distribution function is a stair-step function; i.e., if it is piecewise constant and only increases by discrete jumps.
Nonparametric probability and statistical methods were developed to be used in cases when the researcher does not know the parameters of the distribution of the variable of interest in the population (hence the name nonparametric). In other terms, nonparametric methods do not rely on the estimation of parameters (such as the mean or the standard deviation) describing the distribution of the variable of interest in the population. Therefore, these methods are also sometimes (and more appropriately) called parameter-free methods or distribution-free.
General probability theory related hereto is found in Feller, W. An Introduction to Probability Theory and Its Application, Vol. 1, 3rd Ed. New York: Wiley, 1968. The Theory of Runs (developed later in the disclosure) is described in Mood, A. M. “The Distribution Theory of Runs,” Ann. Math. Statistics 11, 367-392, 1940. It is also noted that recent research has revealed a critical heed for highly sparse data set time distribution analysis methods and apparatus separate and apart from those adapted for treating large sample distributions. P. J. Hoel et al., Introduction to the Theory of Probability, Boston, Houghton-Mifflin, 1971 is incorporated herein by reference. An example of the Runs Test is described in G. H. Moore & W. A. Wallis, 1943, “Time Series Significance Tests Based on Signs of Difference”, Journal of the American Statistical Association, vol. 39, pages 153-164, and is incorporated herein by reference.
Examples of exemplary patents related to the general field of the endeavor of analysis of sonar signals include:
U.S. Pat. No. 5,675,553, issued Oct. 7, 1997, to O'Brien, Jr. et al., discloses a method for filling in missing data intelligence in a quantified time-dependent data signal that is generated by, e.g., an underwater acoustic sensing device. In accordance with one embodiment of the invention, this quantified time-dependent data signal is analyzed to determine the number and location of any intervals of missing data, i.e., gaps in the time series data signal caused by noise in the sensing equipment or the local environment. The quantified time-dependent data signal is also modified by a low pass filter to remove any undesirable high frequency noise components within the signal. A plurality of mathematical models are then individually tested to derive an optimum regression curve for that model, relative to a selected portion of the signal data immediately preceding each previously identified data gap. The aforesaid selected portion is empirically determined on the basis of a data base of signal values compiled from actual undersea propagated signals received in cases of known target motion scenarios. An optimum regression curve is that regression curve, linear or nonlinear, for which a mathematical convergence of the model is achieved. Convergence of the model is determined by application of a smallest root-mean-square analysis to each of the plurality of models tested. Once a model possessing the smallest root-mean-square value is derived from among the plurality of models tested, that optimum model is then selected, recorded, and stored for use in filling the data gap. This process is then repeated for each subsequent data gap until all of the identified data gaps are filled.
U.S. Pat. No. 5,703,906, issued Dec. 30, 1997, to O'Brien, Jr. et al., discloses a signal processing system which processes a digital signal, generally in response to an analog signal which includes a noise component and possibly also an information component representing three mutually orthogonal items of measurement information represented as a sample point in a symbolic Cartesian three-dimensional spatial reference system. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment of whether or not the digital signal comprises solely random noise, and if not, generates an assessment of degree-of-randomness. The noise likelihood determination system controls the operation of an information processing sub-system for extracting the information component in response to the random noise assessment or a combination of the random noise assessment and the degree-of-randomness assessment. The information processing system is illustrated as combat control equipment for submarine warfare, which utilizes a sonar signal produced by a towed linear transducer array, and whose mode operation employs three orthogonally related dimensions of data, namely: (i) clock time associated with the interval of time over which the sample point measurements are taken, (ii) conical angle representing bearing of a passive sonar contact derived from the signal produced by the towed array, and (iii) a frequency characteristic of the sonar signal.
U.S. Pat. No. 5,966,414, issued Oct. 12, 1999, to Francis J. O'Brien, Jr., discloses a signal processing system which processes a digital signal generated in response to an analog signal which includes a noise component and possibly also an information component. An information processing sub-system receives said digital signal and processes it to extract the information component. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment that the digital signal comprises solely random noise, and controls the operation of the information processing sub-system in response to the random noise assessment.
U.S. Pat. No. 5,781,460, issued Jul. 14, 1998, to Nguyen et al., discloses a chaotic signal processing system which receives an input signal from a sensor in a chaotic environment and performs a processing operation in connection therewith to provide an output useful in identifying one of a plurality of chaotic processes in the chaotic environment. The chaotic signal processing system comprises an input section, a processing section and a control section. The input section is responsive to input data selection information for providing a digital data stream selectively representative of the input signal provided by the sensor or a synthetic input representative of a selected chaotic process. The processing section includes a plurality of processing modules each for receiving the digital data stream from the input means and for generating therefrom an output useful in identifying one of a plurality of chaotic processes. The processing section is responsive to processing selection information to select one of the plurality of processing modules to provide the output. The control module generates the input data selection information and the processing selection information in response to inputs provided by an operator.
U.S. Pat. No. 5,963,591, issued Oct. 5, 1999, to O'Brien, Jr. et al., discloses a signal processing system which processes a digital signal generally in response to an analog signal which includes a noise component and possibly also an information component representing four mutually orthogonal items of measurement information representable as a sample point in a symbolic four-dimensional hyperspatial reference system. An information processing and decision sub-system receives said digital signal and processes it to extract the information component. A noise likelihood determination sub-system receives the digital signal and generates a random noise assessment of whether or not the digital signal comprises solely random noise, and if not, generates an assessment of degree-of-randomness. The noise likelihood determination system controls whether or not the information processing and decision sub-system is used, in response to one or both of these generated outputs. One prospective practical application of the invention is the performance of a triage function upon signals from sonar receivers aboard naval submarines, to determine suitability of the signal for feeding to a subsequent contact localization and motion analysis (CLMA) stage.
U.S. Pat. No. 6,397,234, issued May 28, 2002, to O'Brien, Jr. et al., discloses a method and apparatus are provided for automatically characterizing the spatial arrangement among the data points of a time series distribution in a data processing system wherein the classification of said time series distribution is required. The method and apparatus utilize a grid in Cartesian coordinates to determine (1) the number of cells in the grid containing at least-one input data point of the time series distribution; (2) the expected number of cells which would contain at least one data point in a random distribution in said grid; and (3) an upper and lower probability of false alarm above and below said expected value utilizing a discrete binomial probability relationship in order to analyze the randomness characteristic of the input time series distribution. A labeling device also is provided to label the time series distribution as either random or nonrandom, and/or random or nonrandom.
U.S. Pat. No. 5,757,675, issued May 26, 1998, to O'Brien, Jr., discloses an improved method for laying out a workspace using the prior art crowding index, PDI, where the average interpoint distance between the personnel and/or equipment to be laid out can be determined. The improvement lies in using the convex hull area of the distribution of points being laid out within the workplace space to calculate the actual crowding index for the workspace. The convex hull area is that area having a boundary line connecting pairs of points being laid out such that no line connecting any pair of points crosses the boundary line. The calculation of the convex hull area is illustrated using Pick's theorem with additional methods using the Surveyor's Area formula and Hero's formula.
U.S. Pat. No. 6,466,516, issued Oct. 5, 1999, to O'Brien, Jr. et al., discloses a method and apparatus for automatically characterizing the spatial arrangement among the data points of a three-dimensional time series distribution in a data processing system wherein the classification of the time series distribution is required. The method and apparatus utilize grids in Cartesian coordinates to determine (1) the number of cubes in the grids containing at least one input data point of the time series distribution; (2) the expected number of cubes which would contain at least one data point in a random distribution in said grids; and (3) an upper and lower probability of false alarm above and below said expected value utilizing a discrete binomial probability relationship in order to analyze the randomness characteristic of the input time series distribution. A labeling device also is provided to label the time series distribution as either random or nonrandom, and/or random or nonrandom within what probability, prior to its output from the invention to the remainder of the data processing system for further analysis.
U.S. Pat. No. 5,144,595, issued Sep. 1, 1992, to Graham et al., discloses an adaptive statistical filter providing improved performance target motion analysis noise discrimination includes a bank of parallel Kalman filters. Each filter estimates a statistic vector of specific order, which in the exemplary third order bank of filters of the preferred embodiment, respectively constitute coefficients of a constant, linear and quadratic fit. In addition, each filter provides a sum-of-squares residuals performance index. A sequential comparator is disclosed that performs a likelihood ratio test performed pairwise for a given model order and the next lowest, which indicates whether the tested model orders provide significant information above the next model order. The optimum model order is selected based on testing the highest model orders. A robust, unbiased estimate of minimal rank for information retention providing computational efficiency and improved performance noise discrimination is therewith accomplished.
The above cited art, while extremely useful, could be improved with the automated capability of measuring the spatial arrangement for data distributions with a very small number of points, objects, measurements and then labeling nonrandom distributions correctly more often as disclosed utilizing the method taught herein. Consequently, those of skill in the art will appreciate the present invention which addresses these and other problems.